President Barack Obama is about to announce his new strategy for Afghanistan, but the success of whatever option he chooses will depend heavily on Pakistan acting to stop its territory being used to attack Western forces next door. And that’s bad news, because the demands of its own domestic counterinsurgency campaign, doubts about the duration of U.S. commitment in Afghanistan and looming political instability in Islamabad have left Pakistan in no hurry to help out.

Obama’s National Security Adviser General James Jones last week visited Islamabad carrying a message from his boss to Pakistan’s President Asif Ali Zardari. The New York Times reported Monday that in the letter, Obama urged Zardari to rally his nation behind a joint campaign against militants who fight the Pakistani government and those who fight U.S. and allied troops in Afghanistan. Obama was also reported to have demanded more decisive action against al-Qaeda leaders hiding in Pakistan’s tribal areas. In return, he reportedly offered a range of fresh incentives, “including enhanced intelligence sharing and military cooperation.” (See pictures of the battle against the Taliban.)

The problem, of course, is that Obama’s letter may have gone to the wrong address. As a weak and unpopular President scarcely seen in public and now the object of growing vilification at home, Zardari is in no position to lead a popular movement against militancy, much less to redirect his army’s focus. As ever, it is the all-powerful military establishment that will make the key decisions in Pakistan.

Pakistan’s military has certainly moved decisively against those militants that pose a direct challenge to its authority on home soil. Buoyed by its successes in last May’s campaign to drive the Taliban out of the Swat Valley, it has for the past month deployed some 30,000 troops to confront the militants in their main stronghold of South Waziristan, along the Afghan border. The army has steadily cleared territory eastward, seizing some of the Pakistani Taliban’s most prized bases, but also sparking a vicious wave of terrorist attacks that continues to claim innocent lives on a near daily basis. (See pictures of Pakistan’s vulnerable north-west passage.)

The South Waziristan offensive, however, may be the limit of what the Pakistani military is willing to take on right now. It’s priority after clearing the area of Taliban elements will be to hold it — and there are signs that the militants have merely scattered to areas beyond the scope of the current offensive, waiting to stage a return. “We have not been defeated,” Taliban spokesman Azam Tariq told reporters at a secret location on Wednesday, dismissing the army’s claims. “We have voluntarily withdrawn into the mountains under a strategy that will trap the Pakistan army in the area.”

With a long fight ahead of it, the Pakistan army won’t welcome demands that it expand its range of operations. “They will view this letter with some displeasure,” says Hasan Askari-Rizvi, an independent military analyst. “Pakistan army is not going to go to North Waziristan before it completes its operation in South Waziristan.” Two of the militant groups that Washington would like to see Islamabad target are based in North Waziristan: the Haqqani network and the one led by Hafiz Gul Bahadur, both of whom mount cross-border attacks on NATO forces in Afghanistan.

“I don’t think that the Pakistan army will target Haqqani,” adds Askari-Rizvi. “The reason being that they don’t want to open a front with every militant group.” The army has long insisted that it does not have the resources to counter the full range of militants based in the tribal areas. Already, military officials argue, heavy numbers are committed all along the tribal areas and in the Swat Valley. It is also forced to commit forces to guard against upsurges of militancy in other parts of Pakistan. And, of course, the army’s priority remains guarding the eastern border with India. Indeed, the fact that India continues to be viewed as the principal security challenge by the Pakistani military establishment also dictates a policy toward Afghanistan that does little to help the U.S. there.

Pakistan’s generals are concerned by what they perceive as growing Indian influence in Afghanistan, through the Karzai government and massive development projects. They also accuse India of using Afghanistan as a base from which to wage a proxy war on Pakistan. Its priorities make the Pakistan army unlikely to turn its fire on the Haqqani and Hafiz Gul Bahadur networks, as Obama is demanding. Instead, the army has revived a nonaggression pact with Bahadur and with Maulvi Nazir — both of which use Pakistani soil as a base from which to wage war on NATO forces in Afghanistan. Pakistan’s priority is simply to get them to agree to stay neutral or join in the fight between the army and the Pakistan Taliban. Nazir, who was freed from Pakistani custody to fight al-Qaeda-linked Uzbek militants, controls the areas of South Waziristan where the Pakistan army has positioned troops to seal off a line of retreat for the Pakistan Taliban. The danger for the U.S. is that such deals involve a nod and a wink for continued cross-border attacks, making the militants an even more potent threat.

The Haqqani network is believed to have long-standing links with Pakistan’s Inter-Services Intelligence organization, while senior Western diplomats allege that Mullah Omar and the leadership of the Afghan Taliban continues to operate out of the southwestern city of Quetta — a claim furiously denied by Pakistan’s military. Many suspect that the reason that the Afghan Taliban manages to operate unmolested on Pakistani soil is Pakistan’s need to maintain leverage in Afghanistan, where the U.S. presence is viewed as temporary. Indeed, some Pakistani observers suggest that even if a U.S. surge is successful, it will at best lead to a negotiated settlement with the Taliban, in which Pakistan would play broker.

“You need an increased U.S. troop strength to countervail the Taliban in the south and the east, so that you can bring them to the negotiating table,” says retired general Talat Masood. “The Pakistani military also thinks that if they succeed in Afghanistan, the Taliban will be less powerful in Pakistan. The Americans should see Pakistan as an interlocutor for trying to handle these groups politically.”